This question was previously asked in

ISRO Scientist CS 2014 Official Paper

Option 2 : \(\dfrac{(2^{R - 1})V}{(2^R - 1)}\)

ISRO Scientist CS 2020 Official Paper

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80 Questions
240 Marks
90 Mins

The correct answer is **option 2.**

**CONCEPT**

In *DAC (Digital to Analog Converter)*

Every input has a weight and the output voltage is the sum of the weights of 1's in the input.

**EXPLANATION**

If a DAC's maximum output voltage is V volts and the resolution is R bits, then

The least significant bit's weight is \(V \over 2^R -1\)

The second least significant bit's weight is \(2V \over 2^R -1\)

The third least significant bit's weight is \(4V \over 2^R -1\)

The fourth least significant bit's weight is \(8V \over 2^R -1\)

If the maximum output voltage of a Digital to Analogue Converter is V volts and if the resolution is R bits then the weight of the most significant bit is, \(\dfrac{(2^{R - 1})V}{(2^R - 1)}\)

**Hence the correct answer is** \(\dfrac{(2^{R - 1})V}{(2^R - 1)}\)